Profiled Composite Slab Strength Determination Method

Journal of Soft Computing in Civil Engineering 2-2 (2018) 31-55
How to cite this article: Mohammed K, Karim IA, Aziz FNAA, Law TH. Profiled composite slab strength determination method. J
Soft Comput Civ Eng 2018;2(2):31–55. https://doi.org/10.22115/scce.2018.102399.1030
2588-2872/ © 2018 The Authors. Published by Pouyan Press.
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Profiled Composite Slab Strength Determination Method
K. Mohammed1
, I.A. Karim2
, F.N.A.A. Aziz3
, T.H. Law3
1. Senior Lecturer, Department of Civil & Water Resources Engineering, University of Maiduguri, Maiduguri,
Nigeria
2. Senior Lecturer, Department of Civil Engineering, University Putra Malaysia, Serdang, Malaysia
3. Associate Professor, Department of Civil Engineering, University Putra Malaysia, Malaysia
Corresponding author: engrkachalla@unimaid.edu.ng
https://doi.org/10.22115/SCCE.2018.102399.1030
ARTICLE INFO ABSTRACT
Article history:
Received: 27 October 2017
Revised:
Accepted: 05 February 2018
The purpose of this article is to develop a new numerical
approach for determining the strength capacity of a profiled
composite slab (PCS) devoid of the current challenges of
expensive and complex laboratory procedure required for
establishing its longitudinal shear capacity. The new Failure
Test Load (FTL) methodology is from a reliability-based
evaluation of PCS load capacity design with longitudinal
shear estimation under slope-intercept (m-k) method. The
limit-state capacity development is through consideration of
the experimental FTL value as the maximum material
strength, and design load equivalent estimation using the
shear capacity computation. This facilitates the complex
strength verification of PDCS in a more simplified form that
is capable of predicting FTL value, which will aid in
determining the longitudinal shear of the profiled deck
composite slab with ease. The developed strength
determination effectively performs well in mimicking the
probabilistic deck performance and composite slab strength
determination. The strength test performance between the
developed scheme and the experiment-based test results
indicates high similarity, demonstrating the viability of the
proposed strength determination methodology.
Keywords:
Slope-intercept method;
Reliability;
Profiled composite slab;
Longitudinal shear;
First order reliability method;
Strength test.

32 K. Mohammed et al./ Journal of Soft Computing in Civil Engineering 2-2 (2018) 31-55
1. Introduction
Composite action between the profiled sheeting deck and the hardened concrete that comes into
play with effective development of longitudinal shear at the steel-concrete interface give birth to
a popular construction method known as profiled composite slab (PCS)construction. However,
despite the numerous advantages associated with using PCS in the construction industry, costlier
and time-consuming laboratory procedures accounts for its shear characterization [1]. Moreover,
this applies to all the known methods for the determination of its shear bond capacity.
Longitudinal shear capacity defines the ultimate strength of profiled composite slab [2].
However, several factors are known to influence the longitudinal shear capacity of a PCS, and
that hinders the development of a simplified PCS strength determination [3,4]. There is a serious
need to address this drawback. Hence, this paper attempts to develop a longitudinal shear-based
numerical strength determination model for the PCS that considers the randomness associated
with its strength influencing factors.
2. Literature review
The quest for replacing the uneconomical and complex strength verification of composite slab
led to both several numerical and experimental approach studies [5,6]. Abdullah and Samuel
Easterling [5] and Abdullah, Kueh [6]studies result yields the developments of proposals for PCS
shear capacity modeling that takes in to account the slab slenderness function. Abdullah and
Samuel Easterling [5] study experiment similarly show the determination of shear bond-end slip
behavior of composite slab through force equilibrium method. The author’s finite element model
of the slab fails to yield positive result due to modeling limitation because of the strength
influencing factors. Similarly, Abdullah, Kueh [6] study finding also reveals the slab slenderness
function influence on the longitudinal shear bond. The authors have presented the result of linear
interpolation of shear bond that includes the effect of the slenderness and concludes to have
performed satisfactorily in the prediction of the composite slab capacity.
In another PCS study, it shows the simulation results for long slab specimens reflect true
resembles of the slab performance in comparisons with experimental literature findings with the
exception of few where the comparative behavioral analysis for the short span shows behavioral
variations between the model result and experiments [7,8]. Critics of the FE analysis application
for shear bond capacity for composite slab shows that shear bond is geometry dependent, and
this signifies the need to carry out a full-scale test on PCS to be utilized in the FE formulations.
Hence, FE modeling will become uneconomical since the test has to be conducted by utilizing
the data [5]. Therefore, in order to augment this drawback, there is a need to use a different
numerical approach in finding a solution to a simplified PCS strength determination, and the
reliability method is one good option other than finite element approach. Hence, this paper
focuses on using the reliability method in exploring its potentials to curb conservatism in design
and strength verification of PCS.
Reliability method studies on the performance of composite slab are few because very little areas
are covered [9]. The few areas covered are found in the literature [1]. There are numbers of

K. Mohammed et al./ Journal of Soft Computing in Civil Engineering 2-2 (2018) 31-55 33
methods that are useful in determining the strength parameter, for example, the m-k and partial
interaction methods. This study uses slope-intercept (m-k) method for the determination of the
PCS longitudinal shear resistance parameter.
3. Methodology
The m and k parameters are obtained after conducting experimental flexural testing of the
composite slab specimens, and deducing from the linear relationship plots of vertical shear,
t p
V / bd
against the shear bond, p s
A / bl
for two groups of test values of long, X and short, Y
specimens, as depicted in Fig. 1. The standard full-scale laboratory testing procedure for the two
test groups requires a minimum of three test specimens for each long and short shear specimens
as shown in Fig. 1.
x
y
k
?
m
1
0
L
h
t
ls ls
w
b
d
p Ap stresses at failure
vt/bdp
Ap/bls
vt
0.85fck
fyp
1
1
1
1
2
2
3 3
Fig. 1. Typical slope-intercept method laboratory setup [10].
In Fig. 1, p
A
stands for the metal deck effective cross-sectional area and yp
f
represents its yield
strength value. Similarly, the centroids distance is p
d
, and s
l
is the shear span length (normally
taken as / 4
L
, where L is the clear span between supports) [11]. For ductile failure condition,
the support reaction is computed using Eq. (1).
/ 2
t
V w
(1)
However, in cases where it exhibits a brittle failure condition, a factor of 0.8 [12] is applied to
Eq. (1). The ratio
/
s p
l d
’’herein referred to as inverted slenderness in this paper’’ plays a critical
role in defining PCS strength capacity. Hence, the vertical shear stress, t p
V / bd
for composite
slab at equilibrium is
.
p yp
t
p p s s
A f
V m
bd bd l bl
(2)

Johnson [11] study finding reveals that yp
f
has insignificant influence on longitudinal shear
computation. Hence Eq. (2) reduces to Eq. (3).
p
t
u rd
p s
A
V
m k
bd bl ,
( )
(3)
The parameters m and k in Eq. (3) are defined previously, and are determined from full-scale
laboratory procedure as shown in Fig. 1. The t
V
value for a slab width, b  design shear
resistance, ,
i Rd
V
the semi-empirical expression in Eq. (4) is the PCS design shear resistance
function.
, [ ( ) ]
p p
i Rd
s
bd A
V m k
bl
(4)
The shear connection factor had a value of 1.25 [13].
3.1. Failure testing loads
This study uses full-scale experimental laboratory tests results conducted by several authors
[3,14–16] serves as input variables for the failure test load (FTL) in developing the PCS
performance function. Marimuthu, Seetharaman [14] conducted an experimental evaluation of
PCS in accordance to the EC4 standard using M20 grade concrete. The testing shear span lengths
s
l are 320 mm, 350 mm, 380 mm and 850 mm, 950 mm, 1150 mm. Similarly, Hedaoo, Gupta
[16] also carried conducted its experimental testing with Colour Roof India deck span that has
p
A value of 839 mm2
. The author slab specimen (3 m length) has a nominal depth of 102 mm,
width, b of 830 mm, concrete thickness above the flange, c
h and p
d values of 50 mm and 76.77
mm, respectively. Due to temperature and shrinkage effect control, the author placed 6 mm 
mesh at mid concrete depth of 25 mm from the top surface, and similarly conducted the testing in
accordance with EC4 [17] provisions under varying s
l values of 300 mm, 375 mm, 450 mm, 525
mm, 600 mm and 675 mm.
Furthermore, Cifuentes and Medina [3] conducted its experiments using two different galvanized
trapezoidal sheeting desk, MT-60 (AW specimens) and MT100 (BT specimens) with respective
p
A values of 1003 mm2
and 1032 mm2
, and performed the experimental testing procedure
according to EC4 standard. The author uses two shear span lengths both for AW specimen (0.575
m and 1.0 m) and BT specimens (0.75 m and 1.0 m) with each shear span length having three
short and long specimens designated by the third letter in the slab type (Table 1). However, p
d
value varies for both short (103 mm, 123 mm) and long specimens (143 mm, 193 mm) under
both AW and BT specimens. Similarly, Holmes, Dunne [15] uses Conflor 60 steel deck profiled

for the experimental composite shear capacity testing with characteristics p
A value of 765.6 mm2
,
yp
f of 350 N/mm2
, and p
d of 100.4 mm.
However, the authors’ performed the experimental testing in accordance with the EC4
specification, and fitted the slab with 19 mm shear studs, at a value of 450 mm and 900 mm,
respectively, but could not conduct the cyclic loading test as required by the EC4 provision. The
author's reason for not conducting the cyclic test is based on literature findings that reveal that
cyclic loading has insignificant influence on the load carrying capacity of composite slab [14].
Table 1
Longitudinal shear strength parameters from a different experiment.
source Label s
l
mm FTL kN ,
u rd
N/mm2
N/mm2
m k
Marimuthu, Seetharaman [14]
1 320 55.625 0.281
87.956 0.003
2 350 52.191 0.285
3 380 47.340 0.241
4 850 22.612 0.122
5 950 26.920 0.112
6 1150 16.391 0.097
Cifuentes and Medina [3]
AWS-1 575 45.79
AV.
45.86
0.2401
75.026 0.099
AWS-2 575 46.44
AWS-3 575 45.35
AWL-1 1000 47.69
AV.
47.82
0.180a
AWL-2 1000 46.34
AWL-3 1000 49.44
Hedaoo, Gupta [16]
1-3 300 54.301 0.322
81.95 0.046
4-6 375 50.595 0.266
7-9 450 42.650 0.230
10-12 525 37.195 0.204
13-15 600 31.523 0.184
16-18 675 21.109 0.169
Holmes, Dunne [15]
C450 450 86.75 0.712
197.14 0.1602
C900 900 53.02 0.436
Cifuentes and Medina [3]
BTS-1 750 58.70
AV.
59.68
0.409a
189.78 0.058
BTS-2 750 60.58
BTS-3 750 59.77
BTL-1 1000 67.33
AV.
65.76
0.321a
BTL-2 1000 65.56
BTL-3 1000 64.38
a
This value are recomputed from the original data source

Table 1 shows the PCS properties including the FTL values and their respective shear strength
parameters from several full-scale laboratory-testing procedures by different authors. However, a
suspected computational errors in the values of p s
A bl
in Cifuentes and Medina [3] makes it
necessary in re-computing the p s
A bl
values in order to obtain the correct m and k parameters
(Fig. 2). For example in the experiment [3], the AW specimens which has a uniform p
A
and b
values of 1003 mm2
and 927 mm, respectively, and 575 mm, 1.0 m as s
l
for both short and long
specimens should have uniform values of p s
A bl
in both short and long specimens sections;
0.001882 and 0.001082 instead of 0.001793 and 0.001031 values found in the literature. Hence,
the values are recomputed to obtain the m and k parameters as 189.78, 0.058 N/mm2
and 75.02,
0.10 N/mm2
for the BT and AW specimens, respectively.
Fig. 2. m and k parameters determination for AW and BT slabs.
3.2. Reliability analysis
Structural components reliability is by reliability index or safety index, β value and its
relationship with the failure probability is by the expression in Eq.(5) [9,18].
(safety index value)
f
p
(5)
Where is the inverse of the standardized distribution function. For more details on this
formulation, there are numbers of available good literatures [1]. Hence, Fig. 3 depicts the
reliability analysis syntax for a profiled deck composite slab that places focus on the material
load carrying capacity and design load estimation from the shear resistance of composite slab
under the m-k method. The maximum FTL values (in Table 1) represent the ultimate strength
resistance of the material, and the design load computation is of the longitudinal shear strength
capacity of the profiled deck composite slab. Therefore, accounting for the random variability,
the PCS mean resistance, m
Q
is [19,20]
( )
m n n n n
Q Q M F P
(6)
where n
Q
is the nominal resistance, and has a bias factor of 1.0. Similarly, n
M
, n
F
, n
P
are
factors for material fabrication, mean ratio for component geometry and dimension, and

professional factor for approximation, respectively. These factors mean resistance coefficient of
variation, Q
V
is from the expression in Eq. (7).
2 2 2
( )
Q m f p
V v v v
(7)
The parameters, m
v
, f
v
and p
v
are the equivalent corresponding coefficient of variation, COV
for the factors n
M
, n
F
, and n
P
respectively. Hence, the values for the mean COV for these
factors are 1.10, 0.1; 1.0, 0.05 and 1.11, 0.09, and are all normally distributed [9]. Consequently,
this study Q
V
value is 0.14 from the use of the expression in Eq. (7). Ellingwood and Galambos
[21] characterizations are applied to get the COV value and distribution type for the parameters b
and ls as 0.17 and the lognormal distribution. (each with unit bias factor).
Hence, this study limit state is as shown by the expression in Eq. (8).
,
2 i Rd
m
V
Q R Q
L (8)
The parameters ,
i Rd
V
and m
Q
are from the use of Eq. (4) and (6), respectively. Eq. (9) show the
equivalent transformed function of the expression in Eq. (8), and three discrete variables, X(1-3);
FTL, b, and s
l
(see Fig. 3) were identified.
3
[(1 % / 100) (1)] /
* (( / ( (2) * (3) int * 2 * (2) * /
( * 1.25 * 10 )
p p
R X l
Q slope A X X ercept X d
span (9)
4. Result and discussion
Fig. 4 presents the performance index of PCS where r
l represent the ratio of FTL and design
load from the longitudinal shear capacity, and the symbol  stands for shear span length; for
example, 320
 indicates shear span length of 320 mm. Relating to the FTL value source, the
ratios are shown with different graphs from Fig. 4. For example, the ratio of the Marimuthu,
Seetharaman [14] experimental failure test value to the deterministically computed design load is
shown in A, graphs B, C, and D for the respective ratios from Hedaoo, Gupta [16], Cifuentes and
Medina [3] and Holmes, Dunne [15]. It is interesting to study the decking sheet cross-section
variation influence by examining the 3% change in area from 1003 mm2
to 1032 mm2
. Similarly,
the four indents marks on each plot show the influence of the reduced FTL from full test load
value down to 30% decrease in value. This action evaluates the influence of the present capacity
reduction factor of 0.8 that is applied to the failure test load while computing the shear bond
capacity of the profiled deck composite slab [14].

Fig. 3. Performance index determination flow.
As shown in Fig. 4, the result demonstrated a linear elastic relationship between r
l
and  value.
This behavior is not surprising because of the uniform strength value decrease. To establish the
PCS load-carrying capacity, it is essential to relate its bearing capacity to the shear span length
[22]. The peak and lowest points are the upper and lower tails for each  value as demonstrated
in Fig. 4 that shows an increment in the safety indices value as the r
l
value increases (the shorter
the shear span length, the higher the safety value, and vice versa). For example, 1150
 which has
the lengthiest shear span length, has a lower safety value range. However, this may be due to the
reported failure condition during the static and cyclic loading testing during the experiment.
Interestingly, Fig. 4 (A and B) share similar characteristics, although in Fig. 4 (B), the  value
ranges between 300 mm - 675 mm compared to 320 mm - 1150 mm range under Fig. 4 (A).
Additionally, the lowest tail safety value for the safety is from the lengthiest. As illustrated
previously, the behavior is because of the reported failure due to high slip value during the
experimental tests for determining the strength load. Hedaoo, Gupta [16], reported the formation
of flexural cracks which leads to a sudden drop in capacity accompanied by a 3.27 mm slip. The
end slip value, considering the ductile behavior should not be more than 0.5 mm [4].
The failure of the major longer shear length specimen, either in the static or cyclic load test,
happens when the shear span length is relatively close to the mid-span length of the test

specimen. For example in Fig. 4 (B), the failed specimen has a span length of 2.7 m, and
subtracting twice the  value results in moving the load position close to the mid-span. This
action will definitely result in decreasing the load carrying capacity of the composite slab [16].
Decking cross section is a major strength-influencing factor for PCS, and its variation will
significantly shows differences in the load carrying capacity. Adopting the use of a clear
classification for the differential cross-section as illustrated in Fig. 4 (C), which takes into
accounts both variations in cross section and shear span length. For example 575, 1
A

and 1000, 1
A

represent AW – slab specimens with the uniform cross-sectional area, and  values of 575 and
1000 mm, respectively. Hence, it is evident that the AW and BT slabs show similar result
characteristics (Fig. 4 (C)), but the glaring difference in plot compactness compared to plots
illustrated in Fig. 4 (A and B) is due to the variations in shear span lengths and decking sheet
cross-section. The results also show that a 3% change in cross-sectional value of decking sheet
will significantly influence the safety consideration of PCS. In contrast, Johnson [10] showed
that a change in cross-section of about 24% from 1765 mm2
/m has no effect on the longitudinal
shear strength, but the shear lengths under consideration were greater 1000 mm. However, the
author similarly expresses that this might not be the case for a much smaller section. Chen [22]
experimental study shows an increment of about 15.7% of vertical shear on a range of cross-
sectional area similar to those reported previously before the contrasting argument. In that study
experiment, though diameter 19 studs are used as the end anchorage, the test load capacity is
greatly influenced by the shear studs. Hence, this section concludes that irrespective of the
specimen cross section and span length, the safety value decreases with decreasing  value.
Fig. 4. Safety performances in relation to r
l
value.
Cracks propagation triggers a longitudinal shear failure, and this will result in loss of bond
between the composite medium that will lead to brittle failure. This brittle form of failure is
penalized with 20% reduction in the design resistance. In appraising the penalized load bearing

capacity, Fig. 4 (D) shows the reliability indices having an average safety value of 2.2, and is
slightly lower than the 2.9 benchmark. The difference in safety value is because of the limited
shear span length ( 450
 and 900
 ) considered in that experiment, which falls short of the standard
testing requirement.
The other factor apart from the shear span length is the decking sheet characteristics. This study
explores to find the longitudinal shear value behavior from the use of several decking sheets and
Fig. 5 provides an insight. A horizontal shear bond value of 0.3 MPa is within the acceptable
end-slip that exhibits a ductile behavior [5]. Intuitively, the scattered behavior characteristics
illustrated in Fig. 5, which shows a varying safety values between 2 and 3. This behavior is due
to the sheeting deck characteristics difference that includes the s
A
, yd
f
and thickness values
which are known to influence the composite deck's horizontal shear capacity.
Moreover, the results are shown in Fig. 5 provide a guide in choosing upper and lower safety
ranges in relation to r
l
(see Fig. 8). This section concludes that there is a positive linear
correlation between r
l
and  , with shear span length as an indicator (see Fig. 8, 0.05
p  ). It is
pertinent to note that the  values are those that were able to withstand both static and cyclic
load testing. Generally, the relatively longer shear span length commonly fails because of the
harmful effect of cyclic loading test [3].
Fig. 5. Decking sheets characteristics influence the performance index of PCS.
4.1. Section slenderness effect
This study presents safety performance using the sectional inverted slenderness as explained in
the previous section. The correct characterization of the PCS performance index significantly
depends on that function. However, it is also important to take into consideration the differences
in cross sections and yield strengths of the sheeting deck. Therefore, the inverted slenderness is
multiplied with the decking sheet characteristics p yp
A f
. Hence, for simplicity the resulting
product is a function. Fig. 6 shows the predicted performance from different penalized FTL
considerations.

The slenderness value influence on PCS behavior is substantial [6]. The slenderness
classification as found in the literature can be grouped as either slender (with low
/
p s
d l
value)
or compact (with high
/
p s
d l
value) sections. The classification sounds rational, but a clear
definitive boundary between the two still poses a serious challenge. Abdinasir, Abdullah [23]
proposed a ratio of 1 7 but heavily criticized because of the resulting consequences for slender
section design using the result from compact slab testing can be potentially harmful in the
practical sense. The performance depicted in Fig. 6 shows the decking strength diminishes from
the compact region down to the slender case, and there is similar supportive behavior found in
the literature [6]. All performance behavior in Fig. 6 exhibits near uniform trends for all the
strength loads conditions with increased failure chances while the decreasing FTL values. This is
understandable because the decreasing load capacity has little or no influence on the estimated
design load from longitudinal shear capacity.
The two points in Fig. 6 that show a pronounced f
p
value in relation to other established points
are those that fail to withstand the cyclic loading test during laboratory strength testing as
previously reported by the respective authors. The failed longer specimen had failure chances of
17.3 and 20.4% (see Fig. 6 at 80% FTL). Fig. 7 shows the relationship between the f
p
and 
which is on the use of the 12 points that comprise six each of three long and three short test
specimens from the two standard testing results. Fitting exponential trend gives the best fit, and it
shows high correlation, as shown in Fig. 7. The behavior trend exhibited in that Figure is useful
in formulating the numerical strength test function in this study. Hence, it is the conclusion of
this section that decking strength diminishes from the compact region down to the slender
section and decreasing FTL value show minimal influence on the design load estimation from the
developed approach using the longitudinal shear capacity. Similarly, the use of exponential trend
can suitably describe the failure performance estimation of PCS by the decking stiffness function
that includes the cross-section and the slenderness parameter with high assurances.
Fig. 6. Deck characteristics behavior influenced by penalized FTL values.

Fig. 7. Established relation between Deck characteristics behavior and failure probability at current EC4
[17] consideration for FTL in longitudinal strength parameter determination.
4.2. Load capacity model development
This section pulls together all the relevant findings from the previous section, with justifiable
assumption where necessary in developing new FTL estimation function applicable under the m-
k method. This new function will be devoid of the conservative experimental testing procedure
that was mandatory for PCS strength verification.
Fig. 7, shows a high correlation between the performance function and established deck
characteristics where the minimum and maximum experimental FTL values per span length are
5.464 kN, 18.542 kN and 7.036 kN, 18.1 kN from Marimuthu, Seetharaman [14] and [16],
respectively. The s
l
value is principally the determining factor in the adopted classification
(compact and slender). Generally, 4
l can be used to determine s
l
value theoretically [11].
However, the empirical assumption for s
l
as 6
l , though arguably, seems logical. If that is the
case, the minima and maxima values will rightly fall into the 8
l and 6
l range. Therefore, since
the values can be reasonably divided into two groups, the mean minimum, and maximum FTL
values are 6.25 kN and 18.321 kN. Similarly, applying the same principle to obtain their
corresponding mean design load values as 4.885 kN and 11.407 kN, respectively. These values
are the average result of the minimum and maximum design load values of 4.03 kN, 11.853 kN
and 5.74 kN, 10.96 kN. These values are taken for the whole full experimental testing result
because of the shown ductile failure conditions. According to the study load ratio r
l
defined;
those values form 1.28 and 1.61 as the minimum and maximum r
l
ratios.
Fig. 8 clearly shows the significance of r
l
range with the fitted linear regressed line. The fitting
is well suited because assuming equal variance in safety values between the regressed and the
computed; the result shows no significant difference ( 0.086, 22, 0.05)
t dof p
   . The choice

of linear fitting suitably describes the actual data point behavior, though similar quadratic fittings
yield nearly the same result. However, polynomials and cubic fittings give unfavorable
conditions. Similarly, the policy for establishing a lower and upper safety index value of 1.94 and
2.85 by the minimum and maximum r
l
values were defined previously (Fig. 8). These values are
comparable with the 2.9 code specified value for irreversible flexural limit state violation.
However, this latter value is generally shown to be uneven and verified by Honfi, Mårtensson
[24].
In this study, no doubt the upper value is relatively close to the present target safety index of 2.9,
though uneven. In statistics, the central tendency measure between sets of values is the mean
value,  . , and the evaluated lower and upper safety index is 2.4 with SD of 0.41. Though only
two variables are involved in this case, the SD value clearly shows the compactness of the value.
Therefore, a  value of 2.4  0.41 served as a good PCS target safety index representative. The
corresponding to the proposed target safety index is 1.44 (see Fig. 8). The resulting application
of this simple mathematical expression shown in Eq. (10) will yield the PCS strength function
dl r
FTL l
(10)
The dl symbol stands for the design load, and it is worth examining as to how this parameter
relates to decking characteristics. Fig. 9 shows the relationship between dl and  functions and
shows an obvious linear relation. The projected estimation of  value using the best fit shows no
difference( 0.04, 11, 0.05)
t dof p
   . This indicates a high correlation between the pairs.
Hence, the relating function between the decking characteristics and the projected design load is
shown using the expression in Eq.(11).
( 6) / 5.4
dl (11)
Substitute Eq.(11) for Eq.(10), the resulting FTL estimate, per meter width having a span length
l is
0.001 dl lr
FTL f l
(12)
The parameter lr
f
is the load ratio factor and has a value of 1.44 from the use of the proposed
PCS target safety value. Schumacher, Lääne [25] presented a similar approach that will aid in
predicting PCS behavior that utilizes small-scale test with a simple model for determining the
moment-curvature at critical section of a composite slab. However, in that work, the cognizance
of random variability is not taken into consideration, conclusively, the new proposed FTL
estimate, which takes into consideration the span length and the design load, which is dependent
on sheeting deck characteristics, will give a fair estimation of the PCS load carrying capacity. By
moving away from the use of awkward and expensive large-scale tests for PCS strength
determination, the developed model's performance needs to be compared with the experimental
test results for validation.

Fig. 8. Established relation between  and r
l
function depicting evaluated safety index range with the
use of min. and max. r
l
.
Fig. 9. An established function between design load and profiled deck characteristic.
Therefore, the following section of this paper accounts for the experimental work. This
experimental result compares with the numerical function estimation in order to know the
suitability of the expression shown in Eq. (12) in determining PCS failure strength.

5. Experimental test-setup
This experimental study work consists of testing of eight PCS specimens that includes two each
for both long and short shear span lengths of 228 mm, 243 mm, and 305 mm, 320 mm,
respectively. For simplicity, these specimens are identified using notations SS and LS; for
example, SS-228 and LS-305 represent short and long specimen with a shear span length of 228
mm and 305 mm, respectively.
5.1. Materials properties and slab specimen casting
The metal deck has a thickness of about 0.47 mm, and it is 1829 mm long (L), having width (b)
value of 820 mm as shown in Fig. 10. The desired concrete strength is normal grade concrete,
and the mix is prepared using 20 mm aggregate for 120 mm thick concrete. For hydration
control, 5.2 mm mild bars are meshed through at 220 mm both ways and placed 20 mm above
the metal deck.
Fig. 10. Slab specimen.
All the required standard laboratory checks on the mix design prior to concreting are fully
adhered to the ACI-318 standard. The concrete cubes average compressive strength is 28.55
MPa.
5.2. Experimental test set-up
Application of static load is with the use of hydraulic jack where two rollers weighing about 10
kg each are placed on top of the slab specimen with the intention of applying the two-point load
from a cross beam that also weights about 70 kg. The slab overhang length o
l
is 100 mm from
both ends, and its failure mode is determined through an edges (decking sheet and concrete)
placement of linear variable displacement transducers (LVDT) as depicted in Fig. 10. Similar
LVDT's is in place at the mid-span to record the slab deflection (Fig. 12). Data logger-TDS-530
records the hysteresis history, and the testing is halted if the maximum applied load drops by
about 20% or the mid-span deflection value is approaching 30
l [26].

Fig. 11. Specimen experimental test set-up.
Fig. 12. LVDT arrangements.
Experimental testing results are to validate the numerical solution estimation for the strength
capacity determination of PCS. The closeness between the compared results will validate the
suitability of the developed model for strength capacity estimation of PCS. Hence, Fig. 13 shows
the experimental performance of the tested PCS specimens. A maximum strength capacity value
of 45.97 kN is recorded with the shortest shear span length, and the lengthiest shear span test
value gives 27.97 kN. After the maximum peak failure load, an average of 50% unloading peak
load results in a high deflection value. This explains why there is a large jump beyond the peak
load value as shown in Fig. 13.

Fig. 13. Force-deflection relationships under the four shear span lengths.
6. Model verification
This paper demonstrated the application of a more rational approach to defining the safety value
associated with the PCS longitudinal shear (m-k method). This led to the formulation of closed-
form expression for the FTL estimate, as shown in Eq. (12). Testing the function suitability by
comparative analysis with several full-scale laboratory tests value, slab test details and the
experimental strength loads results together with the study's approximate strength load estimates
from the use of expression in Eq. (12) are in Table 2.
Table 2 shows several PCS experiment results, and the details for the items listed can be found in
the literature [4,13,22,27]. Statistically, there is no FTL value difference between the
experimental results compared to the study's new approach in determining the FTL value (Table
2); Mohammed [4] ( 0.150, 10, 0.05
t dof p
  ),Gholamhoseini, Gilbert [13]
( 0.169, 14, 0.05)
t dof p
  and this study 1.490, 6, 0.05
t dof p
  . However, the FTL
values comparisons between the study's approximate estimation and the experimental result
presented in Chen [22] shows a significant variance of 0.05
p This variance is not surprising,
because the resistance offered by the use of shear studs within the specimens might influence the
load-bearing capacity.

Table 2
Failure test load comparative analysis.
Source
Label
Ap
(mm2
)
Fyp
(MPa)
dp
(mm)
ls (mm) l (m)
Experimental
FTL (kN)
Approximate
FTL (kN)
Gholamhoseini,
Gilbert [13]
ST57-4 1434 536 135.9 850 3.4 92.8 111.34
ST57-6 1434 536 135.9 567 3.4 154 166.95
ST55-4 1485 534 134.6 850 3.4 67 113.7
ST55-6 1485 534 134.6 567 3.4 102.5 170.6
ST70-4 1320 544 122.3 775 3.1 84 96.6
ST70-6 1320 544 122.3 517 3.1 116.5 140.35
ST40-4 1248 475 136 775 3.1 74.4 85.92
ST40-6 1248 475 136 517 3.1 122 128.84
Mohammed [4] Slab 1 980 550 93 900 2.7 46.8 37.07
Slab 2 980 550 93 900 2.7 38.1 37.07
Slab 3 980 550 93 900 2.7 49.1 37.07
Slab 4 980 550 93 45 0 2.7 61.9 74.2
Slab 5 980 550 93 450 2.7 63.7 74.2
Slab 6 980 550 93 450 2.7 65.6 74.2
Chen [22] A-1 1170.8 380 55 650 2.6 52.7 26.04
A-3 1170.8 380 55 800 3.2 42.8 26.02
A-5 1170.8 380 55 650 2.6 39.8 26.04
A-2 1561.8 380 55 650 2.6 61 37.74
A-4 1561.8 380 55 1050 4.2 46.9 34.72
Ong and
Mansurt [27]
AA1 1259 550 79 600 2.4 26 58.3
AA2 1259 550 79 600 2.4 26 58.3
AB1 1259 550 99 750 3 35.8 73.1
AB2 1259 550 99 750 3 33.8 73.1
AC1 1259 550 99 990 3 27.9 23.1
THIS STUDY
EXPERIMENT
LS-228 496.7 340 100 228 1.829 45.97 35.31
LS-243 496.7 340 100 243 1.829 41.33 33.32
LS-305 496.7 340 100 305 1.829 33.5 26.54
LS-320 496.7 340 100 320 1.829 27.97 25.29

The shear studs provide sustained shear capacity for a longer period even with the loss of
composite action [27]. This assertion is true, because similar comparisons in FTL estimations
from slab test specimens [27] with end anchorage show similar variance (Table 2). Rana, Uy [26]
recently presented a study on the effect of end anchorage in the composite slab, and the results
were those expected that shows the increase in the load carrying capacity because of the
anchorage effect. This shows the mammoth contribution of shear-studs in increasing the PCS
longitudinal shear capacity. However, use of such shear connectors is uneconomical, and a
simple deck embossing will provide the needed degree of resistance between the decking sheet
and the concrete. Hence, the study has formulated FTL estimate did not take in to account the
shear stud influence. This limitation will definitely form the variation.
Furthermore, though the FTL comparison between the experimental and the model values shows
good results considering the p-value function, but the load model estimation were low in some
cases and vice-versa. This behavior can be attributed to the influence of the shear span length and
the shear stud device used in some of the experimental tests. While the latter influence on the
load model estimation was given previously, that of the shear span length on the safety
performance estimation is further presented using Fig. 14 that considers the two-point load
application. The analogy shows that safety value decreases with increasing shear span length
towards the mid-span. This reveals the need for careful considerations for the lengthier shear
span length value for experimental tests. For example in Table 2, for a span length of 2.5 m
(excluding 0.2 m overhang length), the resulting use of lengthier shear span length of 900 mm
results in moving the load position close to the mid-span, thus decreasing load capacity as shown
with the model estimation. This behavior is similarly demonstrated experimentally where it was
shown that test specimen fails to withstand the cyclic load test because of the load position close
to the mid-span [16].
Fig. 15 presents the shear values comparisons amongst the experimental, theoretical and new
theoretical values as a further test of the statistical significance of this new strength
determination method. The experimental shear values in panels A and B are from the literature,
and this study's experimental shear is under panel C. Similarly, the theoretical shears
computations were obtained from the use of Eq. (4), and as are the corresponding values of the
new theoretical shear from the use of approximate estimate expression with varying FTL
estimates (10%, exact,  20%). However, in this study, the theoretical shear value could not be
computed with the data from Gholamhoseini, Gilbert [13] under Fig. 15(A), because of different
cross sections used in that experiment coupled with the limited sample size required for
longitudinal shear value estimation.

Fig. 14. Shear length influences the safety behavior of PCS.
Analytically, the results in Fig. 15 (B) and (C) show that the six shear groups differ significantly,
(5,30) 2.76, 0.05
F p
 and (5,30) 2.45, 0.05
F p
 respectively, considering the shear values
from the new theoretical value against the experimental and existing theoretical based
computations. A similar analysis with respect to values in Fig. 15(A) with five shear groups
shows a similar result, (4,35) 5.03, 0.05
F p
 .
Interestingly, there is no variance between the experimental shear and the exact shear value
estimates from the new theoretical relation ( 1.47, 11, 0.05)
t dof p
   . A similar analysis of
theoretical shear values gives a similar result with both Bonferroni corrected alpha
( 2.98, 11, 0.05)
t dof p
   . These results are in agreement with previous experiments that
shows the closeness between predicted shear bond strength and experimental shear value [22].
Furthermore, this is clearly validated with the experimental work where the result of numerical
analysis and the experimental value shows no variations [5]. The performance of the developed
model in determining PCS strength capacity is correlating well with the experimental values as
expected.

Fig. 15. Two experimental shear results in comparison with the estimate of new theoretical value. The
experiment works after: (A) Gholamhoseini, Gilbert [13] (B) Mohammed [4] (C) This study experiment.

6.1. Numerical example of longitudinal shear
This section considers the numerical example of the longitudinal shear  estimation with the use
of approximate strength load for determining the m and k parameter, as shown in Table 3. The
slab groups (X and Y) details and its experimental test values for this example can be found in
Johnson [10]. The computed values of  were 0.28, 0.30 and 0.24 N/mm2
, which stands as 0.27
N/mm2
for group X on average. Comparatively, this study's computed value on average is 0.23
N/mm2
, which compares well with the experimental mean value result. A similar comparison
shows similar results for slab group Y. It should be noted that these values are obtained after
plotting the vertical shear against shear bond so as to obtain the m and k parameters needed for
that computation.
Table 3
Longitudinal shear values example.
Group label p
A
(mm2
)
yp
f
(MPa)
p
d
(mm)
s
l
(mm)
l (m) v (kN)
/ p
v bd
(N/mm2
)
/
p s
A bl
X
1-3 1543 353 132 775 3.1 30.65 0.2321 0.00199
4-6 1543 353 112 975 3.9 25.99 0.2321 0.00158
7-8 1543 353 102 1525 6.1 23.64 0.2319 0.00101
Y
1-3 1330 437 112 1000 4.0 27.74 0.2477 0.00133
4-6 1330 437 112 1500 6.0 27.72 0.2475 0.00089
7. Conclusion
Despite the numerous advantages associated with the use of profiled composite slab in the
construction industry, costlier and time-consuming laboratory procedures accounts for its shear
characterization. Deterministically, because of the strength influencing factors, the much-needed
development of a simplified strength function is hindered. This warrants this paper to develop a
more simplified strength function that considers the randomness associated with those
parameters. Interestingly, it is the conclusion of this paper that the suitability of the proposed

target safety value and the new PCS strength determination under m-k method performed as
expected. The litmus test comparison of load capacities (numerical and experimental) result
shows promise for the numerical model in determining the strength capacity of PCS. Similarly,
the behavioral shear results exhibited for the experimental and theoretical values compare well
with the new theoretical estimates. Hence, this signifies the viability of this new PCS strength
determination method, and this will significantly ease the high level of conservatism in
characterizing PCS strength. However, the said behavior may not apply to PCS with shear
transferring devices between the decking sheet and the concrete. Future studies on the
development of FTL values by incorporating shear-transferring devices will be of great interest.
Acknowledgment
The authors will like to thank the Universiti Putra Malaysia for providing full financial support
(GP-IPS/2015/9453400) required for this work.
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